Spin susceptibility in a narrow degenerate band

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Abstract
It has been shown that the static spin susceptibility of the Hubbard model of correlations for a narrow band calculated in the CPA remains finite for any simple-band model and the carrier number, except possibly in the case of a precisely half filled band. We show that this statement is more general and should be true if the Hubbard model could be solved exactly within the alloy analogy approximation. We then consider a model with orbital degeneracy and show that in this case there can be an instability in the susceptibility and we correlate this instability with Hund's rule